Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl = 35.5 u)

Options

A. 1.46
B. 0.46
C. 1.64
D. 64

Explanation

To find the ratio of the density of ammonia (NH₃) to that of hydrogen chloride (HCl) at the same temperature and pressure, we can use the relationship derived from the ideal gas law.

### Step-by-Step Solution:

1. **Understand the Ideal Gas Law**:
The ideal gas law is given by the equation:
\[ PV = nRT \]
where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the gas constant, and \( T \) is temperature.

2. **Relate Density to Molar Mass**:
The number of moles \( n \) can be expressed in terms of mass \( m \) and molar mass \( M \):
\[ n = \frac{m}{M} \]
Substituting this into the ideal gas equation gives:
\[ PV = \frac{m}{M}RT \]
Rearranging this, we find:
\[ P = \frac{mRT}{MV} \]
Since density \( \rho \) is defined as \( \rho = \frac{m}{V} \), we can substitute this into the equation:
\[ P = \frac{\rho RT}{M} \]

3. **Express Density in Terms of Molar Mass**:
Rearranging the equation gives us:
\[ \rho = \frac{PM}{RT} \]
This shows that density is directly proportional to the molar mass \( M \) of the gas when temperature and pressure are constant.

4. **Calculate Molar Masses**:
- For ammonia (NH₃):
- Atomic mass of nitrogen (N) = 14 u
- Atomic mass of hydrogen (H) = 1 u
- Molar mass of NH₃ = \( 14 + (1 \times 3) = 17 \) g/mol

- For hydrogen chloride (HCl):
- Atomic mass of hydrogen (H) = 1 u
- Atomic mass of chlorine (Cl) = 35.5 u
- Molar mass of HCl = \( 1 + 35.5 = 36.5 \) g/mol

5. **Calculate the Ratio of Densities**:
The ratio of the density of ammonia to the density of hydrogen chloride is:
\[ \frac{\rho_{NH₃}}{\rho_{HCl}} = \frac{M_{NH₃}}{M_{HCl}} = \frac{17}{36.5} \]

6. **Perform the Calculation**:
\[ \frac{17}{36.5} \approx 0.46575 \approx 0.46 \]

### Final Answer:
The ratio of the density of ammonia to that of hydrogen chloride at the same temperature and pressure is approximately **0.46**.